The Valuation of Caps, Floors and Swaptions in a Multi-Factor Spot-Rate Model

Abstract

We build a multi-factor model of the term structure of spot interest rates. The stochastic factors are the short-term interest rate and the premia of the future rates over the short-term interest rate. In the three-factor version of the model, for example, the first-factor is the three month LIBOR the second factor is the premium of the first futures LIBOR over spot lIBOR, and the third factor is the incremental premium of the second futures aver the first, The model provides and extension of the longnormal interest rate model of Black and Karasinuski (1991) to multiple factors. each of which can exhibit mean-reversion.